Curvilinear coordinate systems and periodic coordinates

  1. curvilinear coordinate systems and "periodic" coordinates


    we can consider a generic system of curvilinear coordinates in the 2d plane:

    [tex]\rho = \rho(x,y)[/tex]
    [tex]\tau = \tau(x,y)[/tex]

    Sometimes, it can happen that one of the coordinates, say [itex]\tau[/itex], represents an angle, and so it is "periodic". This clearly happens for example, in polar coordinates.

    What are the families of curvilinear coordinates systems in 2d, that have one or more coordinates that are angles?

    I hope the question is not too vague to be answered.
  2. jcsd
  3. Ben Niehoff

    Ben Niehoff 1,682
    Science Advisor
    Gold Member

    Re: curvilinear coordinate systems and "periodic" coordinates

    Any coordinate system whose coordinate lines form closed curves is going to have at least one periodic coordinate. The periodic coordinate doesn't have to represent an "angle", necessarily. For example, in elliptical coordinates, one of the coordinates might represent a parameter for traveling around an ellipse.

    One example that can have two periodic coordinates is the bipolar system.
  4. Re: curvilinear coordinate systems and "periodic" coordinates

    Ok! thanks for your answer Ben.
  5. Bacle2

    Bacle2 1,179
    Science Advisor

    Re: curvilinear coordinate systems and "periodic" coordinates

    Or spherical coordinates, or coordinates in S^n, or on any subspace that "turns on itself" , or is closed.
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